Phononic crystals, as mechanical metamaterials featuring elastic wave bandgaps, can effectively suppress line-spectrum vibration and noise caused by the propagation of elastic waves in aerospace and maritime engineering. However, due to the complex configurations of phononic crystals, it is challenging to rapidly apply them in practical structures and predict their performance accurately. In this study, considering the coupled nature of elastic longitudinal and transverse waves, we propose a rapid prediction method for the elastic wave transmission characteristics of phononic crystals based on homogenization theory. Using transfer matrix methods combined with homogenized equivalent medium theory, the effective elastic modulus and density of the phononic crystals are derived. Taking a cross-hole unit cell as an example, we analyze its vibration transmission characteristics, and validate through simulations and experiments that the homogenization-based equivalent medium approach is accurate and reliable for rapid prediction, thus providing robust theoretical support for the engineering design of vibration-reducing metamaterials.